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natural bundle; natural transformation; natural operator
For natural numbers $r$ and $n$ and a real number $a$ we construct a natural vector bundle $T^{(r),a}$ over $n$-manifolds such that $T^{(r),0}$ is the (classical) vector tangent bundle $T^{(r)}$ of order $r$. For integers $r\ge 1$ and $n\ge 3$ and a real number $a<0$ we classify all natural operators $T_{\vert M_n}\rightsquigarrow TT^{(r),a}$ lifting vector fields from $n$-manifolds to $T^{(r),a}$.
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